ZKPs are pretty complex and I don't fully understand their inner workings, so I'll try to explain the proposal (and potential benefits) and skip how ZKPs actually work

The proposal wants to add zero-knowledge proofs to the Bitcoin base layer through a soft fork. Zero Knowledge Proofs would allow for more complex scripting (allowing you to perform computation off-chain and you can provide a succinct proof it happened on-chain).

It could also enable more layer-2's. I believe the one the author proposed is similar to a roll-up, where users would deposit into a single "ZKP address", and transfer funds to each other off-chain. It's not quite clear what improvements this would offer over classic payment channels.

However, there are a bunch of issues with adding ZKPs to Bitcoin too that would also increase complexity. Verification keys, which are needed to verify ZKPs can be larger than 520 bytes, so you can't include them in a spending script. Thus you would include the hash, and then propagate the key separately. The issue with this is that without the key, you can't verify the transaction, so for a ZKP spend to happen, you'd have to somehow make sure every node on the network has received the verification key. You'd also need to store this key (seemingly permanently) to verify past transactions, which would increase storage requirements.

Generating ZKPs (and verifying individual ZKPs) is also quite computationally expensive. The cost can be reduced by "batching", but you still would only have a limited amount of ZKP-transactions in a single block, because each one can take tens of milliseconds to verify.